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Counting Ordered Patterns in Words Generated by Morphisms

Abstract : We start a general study of counting the number of occurrences of ordered patterns in words generated by morphisms. We consider certain patterns with gaps (classical patterns) and that with no gaps (consecutive patterns). Occurrences of the patterns are known, in the literature, as rises, descents, (non-)inversions, squares and p-repetitions. We give recurrence formulas in the general case, then deducing exact formulas for particular families of morphisms. Many (classical or new) examples are given illustrating the techniques and showing their interest.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00382674
Contributor : Patrice Séébold <>
Submitted on : Sunday, March 24, 2013 - 9:50:22 AM
Last modification on : Friday, June 11, 2021 - 3:34:05 AM
Long-term archiving on: : Tuesday, June 25, 2013 - 2:25:08 AM

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Patrice Séébold, Sergey Kitaev, Toufik Mansour. Counting Ordered Patterns in Words Generated by Morphisms. Integers : Electronic Journal of Combinatorial Number Theory, State University of West Georgia, Charles University, and DIMATIA, 2008, 8, pp.28. ⟨lirmm-00382674⟩

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